What players are currently regular-season-PUP-eligible? (And do they need to be put on the 53-man roster first to go onto reg season PUP? Or is that only necessary for players that you want to bring back from IR?)
A player who is on PUP ("Active/PUP") throughout Camp can be moved to regular season PUP (Reserve/PUP) during cutdowns without ever being a part of the "final" 53-man roster. The requirement for Reserve/PUP eligibility is that the player may not have practiced with the team at all at any time during Camp/pre-season. Any player who has practiced even for a minute is no longer eligible.
The Pats started Camp with only Hightower and Branch on Active/PUP, but both were removed from that list and began practicing over the past couple weeks, so they're no longer eligible for Reserve/PUP.
Active/NFI, Reserve/NFI (Non-Football Injury) is pretty much the same, but, obviously, refers to an injury sustained outside the realm of the NFL. Could be used on a veteran player who accidentally shoots himself in the leg at a nightclub in July, but it's most often used for a rookie who's still recovering from an injury sustained in college, before his entry into the NFL.
Rookie OT Andrew Jelks is currently on Active/NFI and will almost certainly be moved to Reserve/NFI during cutdowns.
UDFA rookie DE, Keionta Davis, is in an interesting situation. He still hasn't been medically cleared to practice after he was discovered to have a bulging disk in his neck at the Combine. That's a non-football injury. The Pats signed him to his first NFL contract a couple days
after the first pre-season game, but didn't put him on the Active/NFI list.
As far as I know. It may have merely been missed by reporters.
However, since he hasn't practiced, that would seem to make him eligible to be moved to Reserve/NFI during cutdowns. I'm not entirely certain of that, but pretty sure.